The more dense random system

Like the previous system, non-zeros are distributed randomly all over the system. This system has a non-zero density of $42.36\%$, which will cause the B&B routine to generate a much larger number of branches. The run-time of the optimization of this system was roughly two days, while the previous system completed in less than an hour. A glance of the system is found in figure 7.3.

Figure 7.3: The more dense random system. $nz=42.36\%$

As one might expect, the optimization of this system is close to hopeless. Some non-zeros may have been relocated, yet, the R matrix is dense. Although this system shows a limitation of what we can possibly optimize, and what we cannot, it is also in a way malplaced. We wouldn't consider using a direct sparse method on this system in the first place. I kept the example anyway, because it's a nice demonstration of something inappropriate for optimization.

Figure 7.4: Ordered ``dense random'' system before and after QR

Solver	KFLOPS
MatLab	722.5
QR	293.7